Effective Annual Rate (EAR) Calculator

Form

Annual interest rate

Compounding frequency

Results

Periodic rate

0%

EAR

0%

1 What is EAR Calculator?
2 How to Use This Calculator
3 Formula Used
4 Variables Explained
5 Worked Example
6 Why Use This Calculator?
7 Common Mistakes
8 Frequently Asked Questions
9 Sources & References
10 Related Calculators

What is EAR Calculator?

The effective annual rate (EAR) expresses the one-year effect of a nominal annual interest rate when interest compounds during the year. It makes rates with different compounding schedules easier to compare on the same annual basis. A 12% nominal rate compounded monthly, for example, produces more than 12% over a year because each month’s interest can itself earn interest.

This page assumes equal periodic compounding with no deposits, withdrawals, fees or changing rate. It reports both the rate per compounding period and the resulting EAR. In deposit advertising, a regulated annual percentage yield may follow specific legal calculation and disclosure rules, so this estimate should not replace the institution’s official APY.

How to Use This Calculator

Enter the nominal annual interest rate as a percentage. Enter 12 for 12%, not 0.12.
Select annual, semiannual, quarterly, monthly, weekly or daily compounding.
Select Calculate. The annual rate is divided by the number of periods to obtain the periodic rate.
The page compounds one plus that periodic rate for the selected number of periods, subtracts one and converts the answer back to a percentage.
Compare products only when the underlying time period, fees, timing and assumptions are consistent.

The frequency choices use 1, 2, 4, 12, 52 and 365 periods per year respectively. The page models discrete compounding rather than continuous compounding.

Formula Used

Periodic rate = nominal annual rate ÷ m

EAR = (1 + nominal annual rate ÷ m)^m − 1

Here m is the number of compounding periods per year. Use rates as decimals inside the formula: 12% becomes 0.12. Multiply the final decimal by 100 to display a percentage.

Variables Explained

Effective annual rate terms
Term	Meaning	Example
Nominal annual rate	Quoted yearly rate before within-year compounding.	12% entered as 12.
m	Number of equal compounding periods in one year.	12 for monthly; 4 for quarterly.
Periodic rate	Nominal rate divided by m.	1% per month for 12% nominal monthly.
EAR	One-year growth rate produced by compounding.	12.683% in the monthly example.

Worked Example

Take a 12% nominal annual rate compounded monthly. There are m = 12 periods, so the monthly periodic rate is 0.12 ÷ 12 = 0.01, or 1%. The annual growth factor is (1 + 0.01)¹² = 1.126825…, and EAR = 1.126825… − 1 = 0.126825….

Converted to a percentage, the page reports 12.683%. On a theoretical USD 1,000 balance with no transactions or fees, that growth factor would produce about USD 1,126.83 after one year. The dollar illustration explains the rate; principal is not an input to the calculator.

Why Use This Calculator?

When the nominal rate is positive, more frequent compounding produces a higher EAR, though the extra increase gets smaller as frequency rises. Annual compounding makes EAR equal the nominal rate. For borrowing, the effective rate describes compounding cost under these assumptions; for saving, it describes growth before taxes or fees.

EAR is especially useful for comparing two quotes that state the same nominal rate but compound on different schedules. It is less useful when account conditions differ materially. Minimum balances, transaction timing, introductory periods and early-withdrawal rules can outweigh a small difference in effective rates, so the percentage belongs beside the full terms rather than replacing them.

Do not compare the result mechanically with an APR or APY whose definition includes different charges, balance methods or legal assumptions. Read the product disclosure. A negative rate can also be modeled above −100%, but its interpretation depends on the contract and may not match consumer-product conventions.

Common Mistakes

Entering 0.12 when the form expects 12 for twelve percent.
Dividing by 12 and then selecting monthly, effectively applying the conversion twice.
Comparing EAR with a nominal rate as though both used the same basis.
Assuming daily means continuous compounding; this page uses 365 discrete periods.
Ignoring fees, promotional periods or variable rates that are absent from the formula.
Calling the result an official APY without checking the applicable disclosure rules.

Frequently Asked Questions

What is the difference between EAR and the nominal rate?

The nominal rate is the quoted annual rate before within-year compounding. EAR applies the selected compounding schedule and shows the resulting one-year percentage change.

Is EAR the same as APY?

They express a similar effective-year idea, but official APY disclosures can be governed by specific rules and account assumptions. Use the institution’s disclosed APY for a regulated product comparison.

Why is monthly EAR higher than the quoted positive rate?

Each month’s interest is added to the balance used for later months. That interest-on-interest effect raises the one-year result above the nominal positive rate.

Does principal change the EAR?

No. Under this formula, EAR depends only on the nominal rate and compounding frequency. Principal changes the dollar amount earned or charged, not the percentage rate.

Can I use the result for a variable-rate account?

Only as a scenario in which the entered nominal rate remains constant for the year. A rate that changes during the year needs a period-by-period calculation.

Sources & References

Mini Calculator provides online calculators for multiple niches including mathematical, financial, Health, informative, Chemistry, physics, statistics, and conversions. You can use any calculator for free without any limits.